Inverses of disjointness preserving operators in finite dimensional pre-Riesz spaces

Abstract

If ℝⁿ is partially ordered by a generating closed cone K, then (ℝⁿ, K) is a pre-Riesz space. We show for a disjointness preserving bijection T on (ℝⁿ, K) that the inverse of T is also disjointness preserving. We prove that for T there is k ∈ ????(b) such that T ^k is band preserving, where b is the number of bands in (ℝⁿ, K), and ????(b) the set of orders of permutations on b symbols.